Question

The area of the triangle on the complex plane formed by the points $z,z+iz$ and $iz$ is 128 . Then the value of $|z|$ is

• A. 12
• B. 16
• C. 18
• D. 17
• E. 19

Answer 1

Answer: (B)

Let $z=x+iy$
$z+iz=(x-y)+i(x+y)$
$iz=-y+ix$
Area of triangle $=\frac{1}{2}\left|\begin{array}{ccc}x& y& 1\\ x-y& x+y& 1\\ -y& x& 1\end{array}\right|=128$
$x(x+y-x)-y(x-y+y)+1$
$\left(x^2-xy+xy+y^2\right)=256$
$xy-xy+x^2+y^2=256$
$x^2+y^2=256$
$\Rightarrow |z{|}^2=256$
$\therefore |z|=16$